Jun Yan, NC State, Well-balanced numerical method for atmospheric flow equations with gravity
ZoomChair: Alina Chertock (chertock@math.ncsu.edu, contact for Zoom access)
Chair: Alina Chertock (chertock@math.ncsu.edu, contact for Zoom access)
Chair: Alen Alexanderian (alexanderian@ncsu.edu, contact for Zoom access)
In 2001, Lasserre introduced a nowadays famous hierarchy of relaxations, called the moment-sums of squares hierarchy, allowing one to obtain a converging sequence of lower bounds for the minimum of a polynomial over a compact semialgebraic set. Each lower bound is computed by solving a semidefinite program (SDP). There are two common drawbacks related to…
If you take a simple finite-dimensional Lie algebra g and tensor it with the Laurent polynomials in one variable, then you will get an infinite-dimensional Lie algebra known as a loop algebra. Affine Lie algebras are the central extensions of such loop algebras and their representations have been of interest to several mathematicians. What happens if we tensor g with…
Chair: Mette Olufsen (msolufse@ncsu.edu, contact for Zoom access)
Chair: Kevin Flores (kbflores@ncsu.edu, contact for Zoom access)
The resurging interest in deep learning is commonly attributed to advances in hardware and growing data sizes and less so to new algorithmic improvements. However, cutting-edge numerical methods are needed to tackle ever larger and more complex learning problems. In this talk, I will illustrate numerical analysis tools for improving the effectiveness of deep learning…
A popular method to approximate a fixed point of a non-expansive map is C is the Krasnoselskii-Mann iteration. This covers a wide range of iterative methods in convex minimization, equilibria, and beyond. In the Euclidean setting, a flexible method to obtain convergence rates for this iteration is the PEP methodology introduced by Drori and Teboulle…
Chair: Tien Khai Nguyen, contact for Zoom access.
Many biological organisms are comprised of deformable porous media, with additional complexity of an embedded muscle. Using geometric variational methods, we derive the equations of motion for the dynamics of such active porous media. The use of variational methods allows to incorporate both the muscle action and incompressibility of the fluid and the elastic matrix…
Chair: Hien Tran (tran@ncsu.edu, contact for Zoom access)
I will discuss stochastic geometry of random concave functions. In particular, I will explain how a "local" stochastic dominance underlies several functional inequalities. Emphasis will be on a notion of shadow systems for s-concave functions and their interplay with functional inequalities. Based on joint works with J. Rebollo Bueno.
Modular tensor categories arise naturally in many areas of mathematics, such as conformal field theory, quantum groups and Hopf algebras, low dimensional topology, representations of braid groups, and they have important applications in condensed matter physics, modeling topological phases of matter. In this talk, I will start by introducing the relevant concepts (modular, braided and…
Two-dimensional crystals have been intensely investigated both experimentally and theoretically since graphene was exfoliated from graphite. Physicists have recently developed the ability to stack one layer on another with a twist angle controlled to the scale of .1 degree with the goal of creating two dimensional materials with desired electronic, optical, and mechanical properties. Unusual…
Mesh-free methods for boundary value problems (BVPs) can be convenient on manifolds where generating a mesh may be difficult or when the manifold is not known explicitly but is determined by data. Moreover, BVPs are important in machine learning since they provide a rigorous method of regularization for many regression problems. In this talk we…
The question of measuring "handedness" is of some significance in both mathematics and in the real world. Propellors and screws, proteins and DNA, in fact *almost everything* is chiral. Can we quantify chirality? Or can we perhaps answer the question: "Are your shoes more left-or-right handed than a potato?" We can begin with the hydrodynamic…
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